Question

The vertices of a triangle are labeled clockwise A(–5, 3), B(6, 1), and C(–2, –3). How could you show that the figure is a right triangle?

Answer 1

Explanation:

When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.

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If you have studied vectors, you can find the dot product of AC with BC:

  AC = (-5, 3) -(-2, -3) = (-3, 6)

  BC = (6, 1) -(-2, -3) = (8, 4)

The dot product is ...

  (-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0

When the dot product of vectors is zero, they are perpendicular.